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# Pattern Recognition Lecture 6: Classification IV

This lecture covers decision trees, feature selection criteria, entropy, and information gain in pattern recognition. Instructor Dr. Dina Khattab teaches this course at Ain Shams University.

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### What is the primary goal of the greedy decision tree learning algorithm?

To select the best feature to split the data

### What is the problem of selecting the best feature to split the data referred to as?

Problem 1: Feature Selection

### How is the classification error calculated in a decision tree?

By calculating the proportion of misclassified instances

### What is the purpose of calculating the entropy in a decision tree?

<p>To measure the impurity of the data</p> Signup and view all the answers

### What is the stopping condition in a decision tree?

<p>When no more splits improve the accuracy</p> Signup and view all the answers

### What is the main difference between the greedy decision tree learning algorithm and other decision tree algorithms?

<p>The greedy algorithm selects the best feature to split the data at each node</p> Signup and view all the answers

### What is the problem of determining when to stop splitting the data referred to as?

<p>Problem 2: Stopping Condition</p> Signup and view all the answers

### What is the entropy when all examples are of the same class?

<p>0</p> Signup and view all the answers

### What is the purpose of calculating the information gain in a decision tree?

<p>To measure the effectiveness of a split</p> Signup and view all the answers

### What is the formula for calculating entropy?

<p>∑ - pi log2 pi</p> Signup and view all the answers

### What is the information gain in the context of decision trees?

<p>Entropy of the parent minus the weighted average entropy of the children</p> Signup and view all the answers

### What is the purpose of the feature split selection algorithm?

<p>To select the feature with the highest information gain</p> Signup and view all the answers

### What is the entropy of the example 'ssss'?

<p>0</p> Signup and view all the answers

### What is the information gain when splitting on the 'Credit' feature?

<p>0.6599</p> Signup and view all the answers

### Why is the decision split on the 'Credit' feature?

<p>Because it has the highest information gain</p> Signup and view all the answers

### What is the entropy of the example 'sf'?

<p>1</p> Signup and view all the answers

### What is the primary objective when choosing feature h*(x) in decision tree learning?

<p>Lowest classification error</p> Signup and view all the answers

### What is the next step after learning a decision stump?

<p>Recursive stump learning</p> Signup and view all the answers

### What is the first stopping condition in decision tree learning?

<p>All data agrees on y</p> Signup and view all the answers

### What is the main characteristic of greedy decision tree learning?

<p>It selects the best feature at each step</p> Signup and view all the answers

### What is the final output of the decision tree prediction algorithm?

<p>A predicted class label</p> Signup and view all the answers

### What is the main idea behind tree learning?

<p>Recursive stump learning</p> Signup and view all the answers

## Study Notes

### Decision Trees

• Step-by-step process for greedy decision tree learning:
• Select a feature to split data
• For each split of the tree, determine whether to make predictions or continue splitting
• Feature selection criteria:
• Entropy and Information Gain

### Entropy and Information Gain

• Entropy: measures the impurity of data
• If all examples are of the same class, entropy = 0
• If examples are evenly split between classes, entropy = 1
• Formula: 𝐸𝑛𝑡𝑟𝑜𝑝𝑦 = ∑ - 𝑝𝑖 log 2 𝑝𝑖
• Information Gain: measures the effectiveness of a split
• Formula: Information Gain = Entropy (parent) - (weighted average) Entropy (children)

### Calculating Information Gain

• Example 1: Credit feature
• Entropy (parent) = 0.9905
• Entropy (excellent) = 0
• Entropy (fair) = 0.8865
• Entropy (poor) = 0.769
• Information Gain = 0.9905 - (0.225)(0) - (0.325)(0.8865) - (0.45)(0.769) = 0.6599
• Example 2: Term feature
• Entropy (3 years) = 0.72
• Entropy (5 years) = 0.88
• Information Gain = 0.9905 - (0.5)(0.72) - (0.5)(0.88) = 0.1905
• Decision: Split on Credit feature since it has the highest Information Gain (0.6599)

### Feature Split Selection Algorithm

• Given a subset of data M (a node in a tree)
• For each feature hi(x):
1. Split data of M according to feature hi(x)
2. Compute classification error OR Information gain split
• Choose feature h*(x) with lowest classification error or highest Information gain

### Recursion and Stopping Conditions

• Tree learning = Recursive stump learning
• Stopping conditions:
1. All data agrees on y
2. Already split on all features

### Prediction Algorithm

• Decision tree prediction algorithm
• Greedy decision tree learning

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